Water Stewardship

Ground Water Resources of British Columbia

Chapter 2 — Origin, Occurrence and Movement of Ground Water

by

M. Wei

2.1 INTRODUCTION

The goal of this chapter is to provide a concise summary of the origin and occurrence of ground water, the basic theory of ground water flow, and basic concepts of ground water systems. This should prepare the reader for the discussions of ground water resources in Chapters 8 through 11.

Chapter 4 discusses the "geology" part of hydrogeology. Here, we will look at the "hydro" part of hydrogeology. We shall see where ground water fits into the hydrologic cycle, and what causes and governs ground water flow.

This chapter is meant to provide neither a rigorous theory of ground water flow nor the fundamentals of ground water resource evaluation. For this, the reader should refer to texts by Walton (1970), Freeze and Cherry (1979), United States Department of Interior (1981), Driscoll (1986), Fetter (1988), Domenico and Schwartz (1990) and more theoretical texts such as Bear (1972), Bear (1979) and Bear and Verruijt (1987). The reader may also refer to the glossary in Appendix 1 to clarify definitions used in developing the concepts in this chapter.

2.2 GROUND WATER AND THE HYDROLOGIC CYCLE

Water continually circulates between the ocean, atmosphere and land. This continual circulation is called the hydrologic cycle. Water that participates in the hydrologic cycle is referred to as meteoric water (e.g., rainwater, river and lake water, and ground water). Water that does not participate in the hydrologic cycle is called connate water. Figure 2.1 shows meteoric water circulates through this cycle.

Out of the total amount of water that evaporates from the ocean and land, about 20% falls as precipitation back onto the land (the remaining 80% falls as precipitation over the ocean). Looking at the land-based portion of the hydrologic cycle, water enters this part of the hydrologic system as precipitation (rain and snow) and most (68%) leaves as evapotranspiration back to the atmosphere. The rest leaves as surface water discharge (31%) and ground water discharge (1%), returning to the ocean.

Within the system, water travels through different routes. Some initially flows overland into channels and eventually into streams before ultimately discharging out to the ocean. Some water will infiltrate into the ground and travel as ground water and either discharge directly into the ocean or back to the land surface into lakes and streams. Water commonly travels both surface and subsurface routes through the system. Ground water is part of the land-based portion of hydrologic cycle and ground water flow is one of the ways through which meteoric water moves through the cycle.

Figure 2.1 Ground water and the hydrologic cycle

2.3 GROUND WATER FLOW

2.3.1 Concept of Hydraulic Head

Ground water flow occurs because of the difference in energy of the water from one point to another. Ground water flows from a point of higher energy to a point of lower energy. The energy of water at a particular point in the ground water system consists of potential energy, elastic energy and kinetic energy. The kinetic energy can be ignored in most cases, however, because the ground water flow velocity is typically very low; kinetic energy is usually considered negligible compared to the potential and elastic energy.

A convenient way to measure the energy of the water is to measure the ground water level or hydraulic head (energy per unit weight of water) in a piezometer, a cased well opened only over a very short section of its length. This opening or intake is the point of measurement. The level to which water rises in the piezometer with reference to a datum such as sea level is the hydraulic head (Figure 2.2). The hydraulic head in the ground water system at the piezometer intake consists of the elevation head (potential energy per unit weight of water) and pressure head (elastic energy) and is shown in Figure 2.2. The sum of the two types of head is the hydraulic head and is mathematically expressed below:

h = z + Ý

where h = hydraulic head [L]
z = elevation head [L]
Ý= pressure head [L]

Figure 2.2 Concept of hydraulic head (h), elevation head (z) and
pressure head (Ý) at point A

2.3.2 Hydraulic Gradient

The difference in hydraulic head between two points implies a hydraulic gradient. The gradient is along the direction of the lower head. The horizontal component of the hydraulic gradient in a given area can be measured by installing three or more piezometers to the same level in the ground, measuring the hydraulic head in each piezometer, and contouring these head values. It follows that the gradient is in the direction perpendicular to the hydraulic head, or equipotential contours, toward the decreasing hydraulic head (Figure 2.3).

Figure 2.3 Horizontal hydraulic gradient

The vertical component of hydraulic gradient at a given location can be measured by installing several piezometers to different depths and measuring the hydraulic head at each piezometer. Ground water flows in the direction of decreasing hydraulic head. Figure 2.4 shows three cases of vertical hydraulic gradient between points A and B: upward (Figure 2.4a), downward (Figure 2.4b), and no vertical gradient (Figure 2.4c). Note that in Figure 2.4b, even though the pressure head at B is greater than at A, the total hydraulic head at A is greater than at B and ground water will flow from A to B. In general, hydraulic gradients have both a horizontal and vertical component.

Figure 2.4 Vertical hydraulic gradient

Hydraulic gradient is the driving force for ground water flow. The gradient direction indicates the potential for ground water flow in that direction. However, the actual flow direction is also governed by the permeability of the porous medium and by the geology, For example, if the aquifer in Figure 2.3 is homogeneous and isotropic with respect to permeability, (i.e. permeability does not vary in space nor in direction), ground water will flow in the direction of the hydraulic gradient (or perpendicular to the equipotential contours). Though the assumption of a homogeneous, isotropic aquifer is often used in practice, especially in sand and gravel, it should be pointed out that ground water flow in anisotropic and heterogenous aquifers would be sub-parallel to the hydraulic gradient. The deviation in direction would depend on the degree of anisotrophy or heterogeneity. This is an important point to remember, especially in flow in fractured bedrock or in ground water contamination studies and subsequent assigning of liability in case of ground water pollution.

2.3.3 Darcy's Law

Ground water flow can be described quantitatively by Darcy's Law which was derived empirically by Henry Darcy from his experiments in 1856 of water flowing through filter sands (refer to Figure 2.5). Darcy observed that for a given sand, the flow increased directly proportional to the difference in hydraulic head and inversely proportional to the length of flow. Darcy's Law can be expressed one dimensionally as:

q = Q/A = -K dh/dl

where Q =flow rate [L3/T]
A =cross-sectional area through which flow occurs [L2]
q =specific discharge, or flow rate Q, through cross-sectional area A [L/T]
K =proportionally constant [L/T]

Figure 2.5 Darcy's experiment

The term dh/dl is the hydraulic gradient [-] and is the driving force for ground water flow (hydraulic gradient is also represented by the term "i"). The negative sign in Darcy's Law, by convention, signifies flow from a higher to a lower head. The proportionality constant called the hydraulic conductivity, is a combined property of the fluid density and viscosity, and the permeability of the porous medium. Hydraulic conductivity is a measure of the ability of the fluid to flow through a porous medium. Darcy's Law is a linear relationship. A change in the hydraulic gradient causes a directly proportional change in the specific discharge.

Hydraulic conductivity is often confused with permeability. However, the latter is a property of the porous medium only, while the former is a property of the porous medium and the fluid. For example, if the Darcy experiment in Figure 2.5 was performed using maple syrup instead of water (keeping everything else the same), the hydraulic conductivity of the system would decrease, but the permeability of the sand would still remain the same. To avoid confusion, the units for reported values of permeability and hydraulic conductivity should always be checked. Permeability has units of [L2] (e.g., cm² or ft²), whereas hydraulic conductivity has units of [L/T] (e.g., m/day or ft/day).

The specific discharge, q, also has units of [L/T]. However, it is important to realize that specific discharge is not the "speed" of ground water flow, but the flow per unit area. The velocity of an actual water particle moving in the experiment in Figure 2.5 will, on average, be much greater than the value of specific discharge, because the water particle travels a tortuous path which is much longer than the macroscopic linearized path from one end of the experiment column to the other (Figure 2.6). The average ground water velocity can be estimated by dividing the specific discharge, q, by the porosity, n: v=q/n where v is the ground water or "Darcy" velocity.

Figure 2.6 Concept of macroscopic and microscopic ground water flow
(after Freeze and Cherry, 1979)

Darcy's Law is valid only for laminar flow at very low velocities. If flow velocities become high and turbulent flow exits, the relationship between specific discharge and hydraulic head gradient becomes non-linear; specific discharge would not be directly proportional to the hydraulic gradient. Since ground water generally moves very slowly (typically up to 1 m/day), Darcy's Law applies in most situations of ground water flow through porous media. Darcy's Law breaks down when turbulent flow occurs, such as in flow through very large fractures, karstic bedrock, or near very high pumping wells.

Darcy's Law forms the basis for all quantitative ground water analyses. Equations for pumping test analysis, ground water infiltration, and contaminant transport all invoke Darcy's Law.

Figure 2.7 Concept of saturated zone, unsaturated zone, capillary fringe
and water table

2.4 WATER TABLE AND THE SATURATED ZONE

Figure 2.7 is a typical section of the subsurface. Below a certain depth, the ground is saturated with ground water. This is the saturated zone. Above this depth, the ground is not saturated, but the pores and fracture spaces in the geologic deposit may contain some water and air. This is the unsaturated or vadose zone. At the top of the saturated zone, (as well as in the vadose zone), the ground water is held in the pores and fracture spaces under tension (negative or vacuum pressure) by capillary forces. This thin saturated layer where water is held under tension is the capillary fringe (Figure 2.7). The pressure head increases from a negative value at the top of the capillary fringe to zero at the bottom of the capillary fringe. The bottom of the capillary fringe layer where the pressure head is zero (h = z) is defined as the water table. The depth to the water table can be measured by measuring the depth to which water stands in a well that just penetrates into the saturated zone (Figure 2.7) The concepts of hydraulic head, hydraulic gradient, and ground water flow apply equally to the vadose zone. Discussions of ground water occurrence and ground water flow in this publication, however, will be focused primarily in the saturated zone.

In areas where a confining layer of low permeability occurs in a more permeable material, a saturated zone may become locally "perched" above the main saturated zone as infiltrating water collects atop this confining layer. This perched ground water zone is called a perched ground water system and the corresponding water table above the confining layer is a perched water table (Figure 2.8).

Figure 2.8 Concept of perched and main ground water systems

2.5 GROUND WATER FLOW SYSTEM

Figure 2.9 shows a model of ground water flow in a ridge and valley terrain bounded at some depth by an impermeable boundary. This model illustrates some notable features of a ground water flow system. The geologic material underlying the ridges and valleys is homogeneous and isotropic with respect to hydraulic conductivity. Several general observations can be made from this model:

1. The water table forms a subdued replica of the topography and its depth beneath the ground surface is greatest in the highlands and least in the lowlands;
2. The ground water flow is downwards in the highlands — this region of the flow system is the recharge area — and upwards in the lowlands — this part of the flow system is the discharge area;
3. The recharge areas are normally much larger than the discharge areas;
4. Ground water flows from the highlands to the lowlands; from the recharge areas to the discharge areas;
5. There are imaginary boundaries beneath the valleys and ridges called ground water divides across which there is no flow.

Figure 2.9 Hubbert's model of ground water flow
(after Hubbert, 1940)

Ground water flow becomes more complex as the topography and geology become more complex. Figures 2.10a and 2.10b show the effect of topography on ground water flow patterns. Figure 2.10b shows that local topography creates local ground water flow systems. The ground water at a greater depth still eventually reaches the major valley through the regional ground water system.

Figure 2.10 Effect of topography on regional ground water flow patterns
(after Freeze and Witherspoon, 1967)

Figure 2.11 shows the effect of geology on the ground water flow patterns. Ground water tends to flow along zones of higher hydraulic conductivity and across zones of lower hydraulic conductivity. If the higher hydraulic conductivity zones are of sufficient permeability and thickness, these zones form aquifers from which ground water can be withdrawn or pumped economically. The lower hydraulic conductivity zones bounding the aquifers form aquitards.

Figure 2.11 Effect of geology on regional ground water flow patterns
(after Freeze and Witherspoon, 1967)

Figure 2.10 depicts the ground water flow system in its natural steady state. That is, ground water flow everywhere in the system remains constant with time. Human activity such as ground water withdrawal through pumping, excavating and diversion of surface water for example may significantly alter the natural flow patterns. These activities cause transient flow where ground water flow in the system changes with time. Eventually the flow system will adjust to a new steady state.

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